Activation Energies for Diffusion in Alloys

The problems involved in calculating correlation factors for diffusion in dilute alloys can be contrasted to those arising in concentrated solid solutions. As one moves from the pure element to the dilute alloy to the concentrated alloy, the calculation becomes progressively more difficult. Because of the complex atom configurations which can occur in concentrated alloys, it usually is not possible to calculate correlation factors in these alloys exactly. Several important simplifications are available in non-dilute random alloys. A large reduction in complexity can be secured by using a random alloy model where each atom is treated as diffusing in a uniform matrix, with the matrix properties being determined by the composition and jump frequencies in the alloy. Resulting equations in this random alloy model can be expressed directly in terms of the experimentally measurable tracer diffusion coefficients with no unknown vacancy jump frequencies appearing. Also these equations have the advantage of being in simple analytic form and not requiring numerical methods to evaluate the correlation factors. These two features make possible the direct expression of the temperature dependence of the correlation factor in terms of the experimental activation energies. Equations are found for AH/AQ in random binary cubic alloys, where AH is the difference between the activation enthalpies for diffusion of the two species and AQ is the difference between the experimentally measured activation energies of the two species. This ratio is never less than unity and can be much larger than unity. Values are plotted for diamond, body-centered cubic and face-centered cubic structures. From the magnitude and composition dependence of AH/AQ, it is concluded that the temperature dependence of the correlation factor cannot by itself explain the difference between the activation energies measured from tracer diffusion and from internal friction in the non-dilute range.